Two recent p-adic approaches towards the (effective) Mordell conjecture

Jennifer S. Balakrishnan*, Alex J. Best, Francesca Bianchi, Brian Lawrence, J. Steffen Müller, Nicholas Triantafillou, Jan Vonk

*Corresponding author for this work

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Abstract

We give an introductory account of two recent approaches towards an effective proof of the Mordell conjecture, due to Lawrence--Venkatesh and Kim. The latter method, which is usually called the method of Chabauty--Kim or non-abelian Chabauty in the literature, has the advantage that in some cases it has been turned into an effective method to determine the set of rational points on a curve, and we illustrate this by presenting three new examples of modular curves where this set can be determined.
Original languageEnglish
Title of host publicationRegulators IV
Subtitle of host publicationAn international conference on arithmetic L-functions and differential geometric methods
EditorsA Chambert-Loir, J-H. Lu, M. Ruzhansky, Y. Tschinkel
Place of PublicationBirkhäuser
PublisherSpringer
Pages31-74
Number of pages44
ISBN (Electronic)978-3-030-65203-6
ISBN (Print)978-3-030-65202-9
DOIs
Publication statusPublished - 2021

Publication series

NameProgress in Mathematics
PublisherSpringer
Volume338
ISSN (Print)0743-1643

Keywords

  • math.NT
  • math.AG

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